It is demonstrated for the first time that the presence of a small number of fast, nonlocal electrons can dramatically change the thickness of and electric field in the near-wall sheath. Even if the density of the nonlocal fast group, nf, is much less than the density of the bulk electrons, nb (nf∼10-5nb), the near-wall potential can increase dramatically resulting in a comparable increase in the sheath thickness. Because of this low fractional density, the average energy (electron temperature Te) of all electrons is little changed from that of the bulk, yet the near-wall potential drop can increase to tens of Te/e. More importantly, due to the nonlocal nature of this group of electrons, the near-wall sheath potential is found to be independent of Te and is determined only by the energy of the fast group.